Big-data computing is perhaps the biggest innovation in computing in the last decade. We have only begun to see its potential to collect, organize, and process data for profitable business ventures. Data mining is a major component of the big data technology and the whole essence is to analytically explore data in search of consistent patterns and to further validate the findings by applying the detected patterns to new data sets. Big Data concern large-volume, complex, growing data sets with multiple, autonomous sources. This paper explores the major challenges of big data mining some of which are as a result of the intrinsically distributed and complex environment and some due to the large, unstructured and dynamic datasets available for mining. We discover that the gradual shift towards distributed complex problem solving environments is now prompting a range of new data mining research and development problems. In this paper also, we have proffered solution to the new challenges of big data mining by a proposition of the HACE theory to fully harness the potential benefits of the big data revolution and to trigger a revolutionary breakthrough in commerce and industry. The research also proposed a three-tier data mining structure for big data that provides accurate and relevant social sensing feedback for a better understanding of our society in real-time. Based on our observations, we recommend a re-visitation of most of the data mining techniques in use today and a deployment of distributed versions of the various data mining models available in order to meet the new challenges of big data. Developers should take advantage of available big data technologies with affordable, open source, and easy-to-deploy platforms